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Pre-trained Language Models (LMs) have become an integral part of Natural Language Processing (NLP) in recent years, due to their superior performance in downstream applications. In spite of this resounding success, the usability of LMs is constrained by computational and time complexity, along with their increasing size; an issue that has been referred to as `overparameterisation'. Different strategies have been proposed in the literature to alleviate these problems, with the aim to create effective compact models that nearly match the performance of their bloated counterparts with negligible performance losses. One of the most popular techniques in this area of research is model distillation. Another potent but underutilised technique is cross-layer parameter sharing. In this work, we combine these two strategies and present MiniALBERT, a technique for converting the knowledge of fully parameterised LMs (such as BERT) into a compact recursive student. In addition, we investigate the application of bottleneck adapters for layer-wise adaptation of our recursive student, and also explore the efficacy of adapter tuning for fine-tuning of compact models. We test our proposed models on a number of general and biomedical NLP tasks to demonstrate their viability and compare them with the state-of-the-art and other existing compact models. All the codes used in the experiments are available at https://github.com/nlpie-research/MiniALBERT. Our pre-trained compact models can be accessed from https://huggingface.co/nlpie.