The AutoML approach aims to deliver peak performance from a machine learning  portfolio on the dataset at hand. A Monte-Carlo Tree Search Algorithm Selection and Configuration (Mosaic) approach is presented to tackle this mixed (combinatorial and continuous) expensive optimization problem on the structured search space of ML pipelines. Extensive lesion studies are conducted to independently assess and compare: i) the optimization processes based on Bayesian Optimization or Monte Carlo Tree Search (MCTS); ii) its warm-start initialization based on meta-features or random runs; iii) the ensembling of the solutions gathered along the search. Mosaic is assessed on the OpenML 100 benchmark and the Scikit-learn portfolio, with statistically significant gains over AutoSkLearn, winner of all former AutoML challenges.