Summary

Mobile handset market is very dynamic, and history has shown that market leaders do not stay in their position for too long. 
Look at Motorola, Sony Ericsson, Siemens, etc.
ZTE's strategy of starting from low end,  local market, and moving up strategy   and branching out with carrier centric customization will make it a strong contender against Samsung and LG.
ZTE has a very good chance to be No. 3  in mobile handset market share leader by 2013.

Analysis

Today Samsung is No.2  and LG is No. 3 in mobile handset market. 
However, only four years ago, Motorola was No. 2, Sony Ericssson  No.3, Siemens no. 4, and Samsung No.5, LG No. 6.   In four years time frame, Samsung and LG have taken over market leading positions of Motorola, Sony-Ericsson, and Siemens.  This shows how dynamic  mobile phone handset market share  change  come about. There is nothing sacred about  Samsung and LG holding onto its current market share positions for  another  four years.   
Mobile phone handset is a game of component sourcing,  low cost product manufacturing, and rapid product turn over (i.e., low cost engineering design).  The rest are straight forward, so to speak.
ZTE has  already  gained  8% market share in mobile handset market, better position than Samsung was  four years ago.   ZTE  is rapidly  gaining market share in China, the largest market in BRIC as well as gaining foothold with European carriers. 
Displacing Sausung's and LG's at the US & European carriers will take a little time for ZTE, but carrier centric customization strategy will help ZTE.     
ZTE comes in with several advantages over its Korean counterparts: 
1. Lower cost engineering   with better caliber:   Chinese engineering labor cost  is a less than 25% of  Korea  with better homogeneous   technical capabilities.  Korean engineering labor is getting tired, worn out,  the pool is limited, and  as a result, both Samsung & LG have begun to use many foreign design talents locally.   
    In Korea, high caliber science students  go to medical colleges.   Only those who cannot enter the  worst of Korean medical college  would opt for the best engineering school.   As a result, the caliber of  engineering graduates  in Korea has been declining, and has been  inferior  to those of China.   
2.  Lower manufacturing labor cost with closer  ties to Taiwanese component sourcing:   ZTE can take advantage of low manufacturing  labor cost of  China.  
 
   Samsung currently makes most of its phones  in its own plant in  Kumi section of Korea.   LG does some out sourcing in Korea as well as in China.  Company cultures of Samsung and LG make them ineffective in running their own manufacturing plant cost effectively in China.  
ZTE also benefits from its closer ties with Taiwanese clans for component sourcing.  
Samsung's and LG's strategy of squeezing its local  component vendor with,  "I win, you lose"  strategy  will backfire against themselves.   Most of Samsung's and LG's profit growth in recent years  has come at the expense of their component vendors'  profit ....   This is NOT the case with Taiwanese component vendors....
3. Most rapidly growing local market: China is the fastest growing mobile handset market in BRIC, and ZTE enjoys its local boy advantage and has been gaining market share in its local market.
Challenges ZTE faces in further growing market share outside of China into Europe and USA is that of "Sales & Marketing".   This  can be overcome with a good sales team, and ZTE is making a gradual head-way.  As evidenced by Samsung &  LG during the past four years,  ZTE's focus onto non-domestic sales  will likely to place ZTE into No. 3 market position by 2013.

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