Dividing the Qayyam al-Layl (Night Prayer) in the Last Ten nights of Ramadhaan

Detailed  materials on the topic by Scholars hafidhahum-Allaah. 

Find here Shiekh Ubayd -hafidhahu-Allaah- 's answer to this question

Quotes from Sheykh Ubayd's answer:

"It is not from the sunnah of the Messenger (sallallahu alaihi wasallam), nor of his rightly guided caliphs, and nor from the actions of the Imams from the blessed generations who were close to the time of the Prophethood, to perform salatul-taraweeh and salatul-at-tahajuud [i.e. in one night]. Rather they only used to perform the prayer once. And what indicates this is ...."

"... Thirdly, it is not permissible to label the people’s division of the night prayer in Ramadaan into two parts, taraweeh and tahajuud, it is not permissible that it is labelled an innovation because masses of the Imams of the Muslims traversed upon this and so it is not permissible to label it as an innovation. To do so would be an injustice and an error. However, to suffice with one salah [congregation] in the last ten days or in all of Ramadaan is more befitting and superior. ..."

Dividing the Taraweeh into Two is an Innovation – Imam al-Albanee: 

See here >>>, http://www.youtube.com/watch?feature=player_embedded&v=z39hE2-2c9g)

Another compilation of the words of some Scholars can be found here

Other Scholars have consider the division of the taraweeh not to be a problem. See here for the fatwah of the al-Lajnatul-daaimah 

Quotes from the answer of the al-Lajna:

" ...ولا بأس أن يزيد في عدد الركعات في العشر الأواخر عن عددها في العشرين الأول ويقسمها إلى قسمين قسما يصليه في أول الليل ويخففه على أنه تراويح كما في العشرين الأول وقسما يصليه في آخر الليل ويطيله على أنه تهجد فقد كان النبي صلى الله عليه وسلم يجتهد في العشر الأواخر ما لا يجتهد في غيرها وكان إذا دخلت العشر الأواخر شمر وشد المئزر وأحيا ليله وأيقظ أهله تحريا لليلة القدر ..."

Wa Allaah 'alam